Answer:
√6 is irrational.
Step-by-step explanation:
The square roots of the others are rational
sqrt 0.16 = 0.4
sqrt 900 = 30
sqrt25 = 6.
Answer:

The solution of the system can be given as (5,-8).
Step-by-step explanation:
Given system of equations:


To solve the given system of equations:
Solution:
We will use substitution to solve the given system.
We will substitute the
values in terms of
from the equation
into the other equation to solve for 
Substituting
into
.
We have:

<em>Using distribution.</em>

<em>Combining like terms.</em>

Adding 6 both sides.


Dividing both sides by 3.

∴ 
<em>Plugging in
into
.</em>
We have,

∴ 
The solution of the system can be given as (5,-8).
Answer:
243 cm^2 + 108 cm^2 = 351 cm^2
Step-by-step explanation:
So, we have a rectangle and two triangles, we know all the sides or angles.
Rectangle: with 9 cm lenght 15cm + 12 cm = 27 cm
Formula: A=wl -> A=9*27 = 243 cm^2
Trianlge: A=ab/2
Angle 90°
Side A 12 cm
Side B 18 cm - 9 cm = 9 cm
A=ab/2=12·9/2=54 cm times 2 (for the opposite side) = 108 cm^2 = 351 cm^2
First from the information we have, we see that the volume of the cube is 27cm3. So what are the dimensions of its length, width and height? This information will help us to determine the dimensions of the square pyramid.
Volume of a cube is found from the formula V = a3
Where V is volume, and a is the length of one side.
We expand this equation to be:
V= a * a * a
Since all sides of a cube are equal, then this equation will be:
27 = 3 * 3 * 3
Now we know the length width and height of the cube.
Volume of a square pyramid is given by the formula V =1/3ah
Where V is the volume, a is the area of the base of the pyramid, h is the height of the pyramid.
Since it fits perfectly into the cube, then its dimensions are the same as the cube, so:
Area of the base is Length * Width so:
a = 3 * 3 = 9
and height:
h = 3
Now therefore:
V = 1/3 * 9 * 3
V = 1/3 * 27
V = 27/3
V = 9 cm3
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